{
  "id": 3949,
  "curve_key": "-2821310024599400031852559391:-1029557048045654800305624448918468209938257",
  "ainvs": [
    "1",
    "0",
    "0",
    "58777292179154167330261654",
    "1191616953756549805868821004651060172196"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    6
  ],
  "naive_height": 193.4754051301043,
  "faltings_height": 14.183561571924157,
  "conductor": "31566406933966762584842830",
  "bad_primes": [
    "2",
    "5",
    "11",
    "13",
    "19",
    "37",
    "61",
    "73",
    "181",
    "223",
    "307",
    "317",
    "787",
    "2281"
  ],
  "discriminant": "-626414786585853603408468118439385341122779965485497313373089295914995933868195840",
  "regulator": "9573157716.14154920075581948639462994360303070162878758",
  "points": [
    [
      "10798964783028",
      "55549077884036371270"
    ],
    [
      "-2532103995272172/841",
      "766356387598490901019870/24389"
    ],
    [
      "407724103046382420/67081",
      "-731651695983946010481057886/17373979"
    ],
    [
      "1650341559380152/9",
      "67109170994051133619190/27"
    ],
    [
      "-354783418845403308/120409",
      "1316528334941854602676828306/41781923"
    ],
    [
      "-4835488527740218248/552049",
      "-893727691063318172691777106/410172407"
    ],
    [
      "1575885813559474797396/41434969",
      "64477707423990244296455505296494/266716895453"
    ],
    [
      "236965581584207538360/6713281",
      "3780806718237665813689914911294/17394111071"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3843 (source contributor: dujella). Source equation and witness provenance are credited to that entry. Exact rank 8: 8 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.",
  "created_at": "2026-10-05 04:32:37",
  "updated_at": "2026-10-05 04:32:37"
}